It depends, in part, on if you are using the Subject+Modifier convention or not and traditional meanings or not. I follow the convention and the tradition unless there are strong indicators otherwise.
The traditional meanings are:
Snake - "is a sign of misfortune that is ruled by whether the card is close to or far from the person, but it always brings along hypocrisy, treason and loss."
Dog - "very near, assures a faithful one; friendship; very far it indicates treason; surrounded by clouds it warns one not to trust those that call themselves our friends. ["clouds" can indicate any negative card.]
So we have Treason+Treason. This person, probably a woman (Queen of Clubs), is not to be trusted. I would consider whether it is someone trying to ingratiate themselves to you for nefarious reasons (and does not have to be a friend). This person may act nice for bad reasons.
However, if these cards were surrounded by other good cards (Sun, Moon, Bouquet, Key, etc.) then I would consider whether the more modern meaning of Snake as a "wise woman" who is friendly and loyal wouldn't trump the old meanings. I had a Grand Tableau with precisely this situation and the Snake person - a woman - was, indeed, a very wise and loyal friend (who wears glasses - another modern convention).
To me, Dog+Snake would mean to distrust someone I consider a friend - a treasonous or hypocritical friend. The person wouldn't necessarily be a woman.
Snake can also be a rival. If the Dog/Snake combination came up near your significant other, I'd wonder if your partner is cheating on you with your (or his/her) best friend.
